Prediction of cutting forces in helical milling process

The prediction of cutting forces is important for the planning and optimization of machining process in order to reduce machining damage. Helical milling is a kind of hole-machining technique with a milling tool feeding on a helical path into the workpiece, and thus, both the periphery cutting edges and the bottom cutting edges all participated in the machining process. In order to investigate the characteristics of discontinuous milling resulting in the time varying undeformed chip thickness and cutting forces direction, this paper establishes a novel analytic cutting force model of the helical milling based on the helical milling principle. Dynamic cutting forces are measured and analyzed under different cutting parameters for the titanium alloy (Ti–6Al–4V). Cutting force coefficients are identified and discussed based on the experimental test. Analytical model prediction is compared with experiment testing. It is noted that the analytical results are in good agreement with the experimental data; thus, the established cutting force model can be utilized as an effective tool to predict the change of cutting forces in helical milling process under different cutting conditions.     

Prediction of dynamic cutting force and regenerative chatter stability in inserted cutters milling

Currently, the modeling of cutting process mainly focuses on two aspects: one is the setup of the universal cutting force model that can be adapted to a broader cutting condition; the other is the setup of the exact cutting force model that can accurately reflect a true cutting process. However, there is little research on the prediction of chatter stablity in milling. Based on the generalized mathematical model of inserted cutters introduced by ENGIN, an improved geometrical, mechanical and dynamic model for the vast variety of inserted cutters widely used in engineering applications is presented, in which the average directional cutting force coefficients are obtained by means of a numerical approach, thus leading to an analytical determination of stability lobes diagram (SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut is also created to satisfy the special requirement of inserted cutter milling. The corresponding algorithms used for predicting cutting forces, vibrations, dimensional surface finish and stability lobes in inserted cutter milling under different cutting conditions are put forward. Thereafter, a dynamic simulation module of inserted cutter milling is implemented by using hybrid program of Matlab with Visual Basic. Verification tests are conducted on a vertical machine center for Aluminum alloy LC4 by using two different types of inserted cutters, and the effectiveness of the model and the algorithm is verified by the good agreement of simulation result with that of cutting tests under different cutting conditions. The proposed model can predict the cutting process accurately under a variety of cutting conditions, and a high efficient and chatter-free milling operation can be achieved by a cutting condition optimization in industry applications.     

Modelling, simulation and experimental investigation of cutting forces during helical milling operations

The kinematics of helical milling on a three-axis machine tool is first analysed. An analytical model dealing with time domain cutting forces is proposed in this paper. The cutting force model is established in order to accurately predict the cutting forces and torque during helical milling operations as a function of helical feed, spindle velocity, axial and radial cutting depth and milling tool geometry. The forces both on the side cutting edges and on the end cutting edges along the helical feed path are described by considering the tangential and the axial motion of the tool. The dual periodicity which is caused by the spindle rotation, as well as the period of the helical feed of the cutting tool, has been included. Both simulation and experiments have been performed in order to compare the results obtained from modelling with experiments.     

螺旋铣孔工艺的切削稳定性及工艺参数规划

以螺旋铣孔工艺时域解析切削力建模、时域与频域切削过程动力学建模、切削颤振及切削稳定性建模为基础,研究了螺旋铣孔的切削参数工艺规划模型和方法。切削力模型同时考虑了刀具周向进给和轴向进给,沿刀具螺旋进给方向综合了侧刃和底刃的瞬时受力特性;动力学模型中同时包含了主轴自转和螺旋进给两种周期对系统动力学特性的影响,并分别建立了轴向切削稳定域和径向切削稳定域的预测模型,求解了相关工艺条件下的切削稳定域叶瓣图。在切削力和动力学模型基础之上,研究了包括轴向切削深度、径向切削深度、主轴转速、周向进给率、轴向进给率等切削工艺参数的多目标工艺参数规划方法。最后通过试验对所规划的工艺参数进行了验证,试验过程中未出现颤振现象,表面粗糙度、圆度、圆柱度可以达到镗孔工艺的加工精度。     

Improved dynamic cutting force model in ball-end milling. Part I: theoretical modelling and experimental calibration

An accurate cutting force model of ball-end milling is essential for precision prediction and compensation of tool deflection that dominantly determines the dimensional accuracy of the machined surface. This paper presents an improved theoretical dynamic cutting force model for ball-end milling. The three-dimensional instantaneous cutting forces acting on a single flute of a helical ball-end mill are integrated from the differential cutting force components on sliced elements of the flute along the cutter-axis direction. The size effect of undeformed chip thickness and the influence of the effective rake angle are considered in the formulation of the differential cutting forces based on the theory of oblique cutting. A set of half immersion slot milling tests is performed with a one-tooth solid carbide helical ball-end mill for the calibration of the cutting force coefficients. The recorded dynamic cutting forces are averaged to fit the theoretical model and yield the cutting force coefficients. The measured and simulated dynamic cutting forces are compared using the experimental calibrated cutting force coefficients, and there is a reasonable agreement. A further experimental verification of the dynamic cutting force model will be presented in a follow-up paper.     

钛合金大直径孔螺旋铣削工艺优化研究

本文基于螺旋铣孔技术,采用正交试验和极差值分析方法,在钛合金上进行了19.05mm直径孔的螺旋铣削试验。分析了不同切削参数对轴向切削力、钛合金孔径、粗糙度等的影响,以此为指标优化出最佳工艺参数。在此基础上研究了最佳参数下切削力、加工质量和刀具磨损随加工孔数的变化,发现在大直径孔加工中,螺旋铣孔技术可有效改善加工质量、提高加工效率。     

Investigation of the milling stability based on modified variable cutting force coefficients

The cutting force signal distortion is caused by the dynamic characteristics of cutting force testing system. In order to handle this issue, we propose two improvements in the traditional inverse filtering technology. Firstly, we use three-spline interpolation method instead of the curve fitting method to fit the frequency response function of the test system which basically improves the accuracy of fitting. Secondly, the low-pass filter is added before the inverse filter to eliminate the influence of the high-frequency noise signal on the cutting force signal. We choose the cavity-free surface of outer covering parts of mold of automobile as research objects. The inverse filter dynamic compensation technology has been used to remove the influence of the dynamic characteristics of the test system and the high-frequency noise on the cutting force signal. The effectiveness of the proposed method is verified by relative milling experiments. Based on the experimentally measured forces after dynamic compensation, the modified cutting force coefficients are obtained using the average milling force method. The variation law of the cutting force coefficients with the axial depth, the radial width, and the feed rate is examined. Based on the modified variable cutting force coefficients, the 3D stability of the ball end milling cutter surface has been obtained using full-discretization approach. Combining the results from the cutting experiment and the nonlinear method, the stability prediction based on the modified variable cutting force coefficient can improve the prediction accuracy. The results provide theoretical support for the optimization of the machining process of the cavity-free surface of outer covering parts of mold of automobile.     

Improved dynamic cutting force model in peripheral milling. Part II: experimental verification and prediction

Cutting trials reveal that a measure of cutter run-out is always unavoidable in peripheral milling. This paper improves and extends the dynamic cutting force model of peripheral milling based on the theoretical analytical model presented in Part I [1], by taking into account the influence of the cutter run-out on the undeformed chip thickness. A set of slot milling tests with a single-fluted helical end-mill was carried out at different feed rates, while the 3D cutting force coefficients were calibrated using the averaged cutting forces. The measured and predicted cutting forces were compared using the experimentally identified force coefficients. The results indicate that the model provides a good prediction when the feed rate is limited to a specified interval, and the recorded cutting force curves give a different trend compared to other published results [8]. Subsequently, a series of peripheral milling tests with different helical end-mill were performed at different cutting parameters to validate the proposed dynamic cutting force model, and the cutting conditions were simulated and compared with the experimental results. The result demonstrates that only when the vibration between the cutter and workpiece is faint, the predicted and measured cutting forces are in good agreement.     

Modeling and Analytical Solution of Chatter Stability for T-slot Milling

T-slot milling is one of the most common milling processes in industry. Despite recent advances in machining technology, productivity of T-slot milling is usually limited due to the process limitations such as high cutting forces and stability. If cutting conditions are not selected properly the process may result in the poor surface finish of the workpiece and the potential damage to the machine tool. Currently, the predication of chatter stability and determination of optimal cutting conditions based on the modeling of T-slot milling process is an effective way to improve the material removal rate(MRR) of a T-slot milling operation. Based on the geometrical model of the T-slot cutter, the dynamic cutting force model was presented in which the average directional cutting force coefficients were obtained by means of numerical approach, and leads to an analytical determination of stability lobes diagram(SLD) on the axial depth of cut. A new kind of SLD on the radial depth of cut was also created to satisfy the special requirement of T-slot milling. Thereafter, a dynamic simulation model of T-slot milling was implemented using Matlab software. In order to verify the effectiveness of the approach, the transfer functions of a typical cutting system in a vertical CNC machining center were measured in both feed and normal directions by an instrumented hammer and accelerators. Dynamic simulations were conducted to obtain the predicated SLD under specified cutting conditions with both the proposed model and CutPro?. Meanwhile, a set of cutting trials were conducted to reveal whether the cutting process under specified cutting conditions is stable or not. Both the simulation comparison and experimental verification demonstrated that the satisfactory coincidence between the simulated, the predicted and the experimental results. The chatter-free T-slot milling with higher MRR can be achieved under the cutting conditions determined according to the SLD simulation.     

Cutting forces prediction in generalized pocket machining

Cutting force prediction is important for the planning and optimization of machining process. This paper presents an approach to predict the cutting forces for the whole finishing process of generalized pocket machining. The equivalent feedrate is introduced to quantify the actual speed of cutting cross-section in prediction of cutting force for curved surface milling. For convenience, to analyze the process with varying feed direction and cutter engagement, the milling process for generalized pocket is discretized into a series of small processes. Each of the small processes is transformed into a steady-state machining, using a new approximation method. The cutting geometries of each discrete process, i.e., feed direction, equivalent feedrate per tooth, entry angle, and exit angle are calculated based on the information refined from NC code. An improved cutting force model which involves the effect of feed direction on cutting forces prediction is also presented. A machining example of a freeform pocket is performed, and the measured cutting forces are compared with the predictions. The results show that the proposed approach can effectively predict the variation of cutting forces in generalized pocket machining.     

New mathematical method for the determination of cutter runout parameters in flat-end milling

The cutting force prediction is essential to optimize the process parameters of machining such as feed rate optimization, etc. Due to the significant influences of the runout effect on cutting force variation in milling process, it is necessary to incorporate the cutter runout parameters into the prediction model of cutting forces. However, the determination of cutter runout parameters is still a challenge task until now. In this paper, cutting process geometry models, such as uncut chip thickness and pitch angle, are established based on the true trajectory of the cutting edge considering the cutter runout effect. A new algorithm is then presented to compute the cutter runout parameters for flat-end mill utilizing the sampled data of cutting forces and derived process geometry parameters. Further, three-axis and five-axis milling experiments were conducted on a machining centre, and resulting cutting forces were sampled by a three-component dynamometer. After computing the corresponding cutter runout parameters, cutter forces are simulated embracing the cutter runout parameters obtained from the proposed algorithm. The predicted cutting forces show good agreements with the sampled data both in magnitude and shape, which validates the feasibility and effectivity of the proposed new algorithm of determining cutter runout parameters and the new way to accurately predict cutting forces. The proposed method for computing the cutter runout parameters provides the significant references for the cutting force prediction in the cutting process.     

Extracting cutting constants via harmonic force components for a general helical end mill

Mechanistic cutting constants serve well in predicting milling forces, monitoring the milling process as well as in helping to understand the mechanistic phenomena of a machining process for a unique pair of workpiece and cutter materials under various types of cutting edge geometry. This paper presents a unified approach in identifying the six shearing and ploughing cutting constants for a general helical end mill from the dynamic components of the measured milling forces in a single cutting test. The identification model is first presented assuming the milling force is measured with a known phase angle of the cutter spindle. When the phase angle of the cutter rotation is not available, as is the case for most milling machines, it is shown that the true phase angle can be identified through the theoretical phase relationship between the different harmonic components of the milling forces measured with an arbitrary phase angle. The numerical simulation and the experimental results for ball and cylindrical end mills are presented to demonstrate and validate the identification methods.     

Modeling of cutting forces in helical milling by analysis of tool contact angle and respective depths of cut

Knowledge of the behavior and magnitude of cutting forces is very important for correctly calculating cutting power and for obtaining tight tolerances and low levels of tool wear. In this way, the appropriate prediction of the force components collaborates with the correct choice of the cutting parameters and strategies. High oscillation of force values in helical milling increase the relevance of the analysis. In this context, present work describes an approach for modeling cutting forces in helical milling based on the analysis of tool contact angle and the respective depths of cut. From the model, it is possible to predict the behavior and magnitude of the force acting on the insert, which contributes to better process planning. The results indicated a good fit of the experimental values with the models, despite the observation of some errors, which occurred mainly due to the dynamics of the machine and the used approximations.     

螺旋棒铣刀铣削力建模与仿真

在对螺旋棒铣刀铣削力建模中考虑了切削厚度变化对铣削力影响的指数关系、铣刀偏心对实际切削厚度、切入与切出角、铣削力波动的影响,并提出采用实测各刀齿铣削最大值比求解铣刀偏心和识别铣削力系数的方法。在考虑铣刀偏心因素的情况下仿真与实测的铣削力达到非常好的一致性。提出的铣削力仿真方法充分反映了铣削力的实际状态,提高了铣削力仿真精度。     

基于斜角切削理论的钛合金螺旋铣孔切削力建模

通过分析螺旋铣孔的加工原理和计算加工过程中的运动向量,结合侧刃和底刃对切削力的影响,建立了螺旋铣孔过程的切削力解析模型。提出了基于斜角切削的切削力系数辨识方法,并根据斜角切削过程几何关系推导出摩擦角、剪切角、剪切应力的约束方程。开展切削力系数辨识试验和钛合金螺旋铣孔试验对仿真值进行验证,结果表明,切削力的仿真值与试验值误差较小,平均误差为9.55%,从而验证了斜角切削系数辨识方法的有效性和切削力模型的正确性。     

Three dimensional cutting force analysis in end milling

The analysis of cutting forces plays an important part in the design of machine tool systems as well as in the planning, optimization, and control of machining processes. This paper presents a three-dimensional model of cutting forces in peripheral end milling in terms of material properties, cutting parameters, machining configuration, and tool/work geometry. Based on the relationship of the local cutting force and the chip load, the total cutting force model is established via the angle domain convolution integration of the local forces in the feed, cross feed, and axial directions. The integration is taken along the cutter axis and summarized across the cutting flutes. The convolution integral leads to a periodic function of cutting forces in the angle domain and an explicit expression of the dynamic cutting force components in the frequency domain. The closed-form nature of the expressions allows the prediction and optimization of cutting forces to be performed without the need of numerical iterations. To assess the fidelity of the analytical model, experimental data from end milling tests are presented in the context of three dimensional time waveforms, power spectra, and phase angles, in comparison to the values predicted by the model.     

基于数字化加工的铣削力预测系统的开发

切削用量的实时获取是切削力预测的关键技术之一。基于数字化加工技术,通过在加工仿真过程中对三维实体图形进行分析,获得实时的切削参数,实现了切削力的实时预测;开发了一个针对铣削加工的切削力预测软件系统,通过铣削试验验证了该系统的正确性。     

Cutting force model considering tool edge geometry for micro end milling process

The analysis of the cutting force in micro end milling plays an important role in characterizing the cutting process, as the tool wear and surface texture depend on the cutting forces. Because the depth of cut is larger than the tool edge radius in conventional cutting, the effect of the tool edge radius can be ignored. However, in micro cutting, this radius has an influence on the cutting mechanism. In this study, an analytical cutting force model for micro end milling is proposed for predicting the cutting forces. The cutting force model, which considers the edge radius of the micro end mill, is simulated. The validity is investigated through the newly developed tool dynamometer for the micro end milling process. The predicted cutting forces were consistent with the experimental results.     

Speed-varying cutting force coefficient identification in milling

Accurate simulation of the machining process is crucial to improve milling performance, especially in High-Speed Milling, where cutting parameters are pushed to the limit.Various milling critical issues can be analyzed based on accurate prediction of cutting forces, such as chatter stability, dimensional error and surface finish. Cutting force models are based on coefficients that could change with spindle speed. The evaluation of these specific coefficients at higher speed is challenging due to the frequency bandwidth of commercial force sensors. On account of this, coefficients are generally evaluated at low speed and then employed in models for different spindle speeds, possibly reducing accuracy of results.In this paper a deep investigation of cutting force coefficient at different spindle speeds has been carried out, analyzing a wide range of spindle speeds: to overcome transducer dynamics issues, dynamometer signals have been compensated thanks to an improved technique based on Kalman filter estimator. Two different coefficients identification methods have been implemented: the traditional average force method and a proposed instantaneous method based on genetic algorithm and capable of estimating cutting coefficients and tool run-out at the same time.Results show that instantaneous method is more accurate and efficient compared to the average one. On the other hand, the average method does not require compensation since it is based on average signals. Furthermore a significant change of coefficients over spindle speed is highlighted, suggesting that speed-varying coefficient should be useful to improve reliability of simulated forces.     

Prediction of cutting forces along Pythagorean-hodograph curves

This paper proposes a new approach to predicting cutting forces in milling operations. The approach attempts to find the analytic relationship between cutting forces and the tangential direction of the tool path when a tool moves along an analytical curve, i.e., a Pythagorean-hodograph curve that describes a group of analytic curves with special properties, in a milling operation. In conventional methods for the prediction of cutting forces in milling operations, cutting forces are estimated by considering such cutting parameters as feed rate, depth of cut, and tool geometry. However, the change in the moving direction of the cutter, which has a major effect on cutting forces, is often neglected by previous researchers. This work aims to establish the theoretical basis to show how cutting forces along a curve can be predicted. Two case studies are used to illustrate the proposed cutting force prediction strategy.